Persistence Probabilities of a Smooth Self-Similar Anomalous Diffusion Process.

We consider the persistence probability of a certain fractional Gaussian process M H that appears in the Mandelbrot-van Ness representation of fractional Brownian motion. This process is self-similar and smooth. We show that the persistence exponent of M H exists, is positive and continuous in the Hurst parameter H. Further, the asymptotic behaviour of the persistence exponent for H ↓ 0 and H ↑ 1 , respectively, is studied. Finally, for H → 1 / 2 , the suitably renormalized process converges to a non-trivial limit with non-vanishing persistence exponent, contrary to the fact that M 1 / 2 vanishes. [ABSTRACT FROM AUTHOR]